In the next five problems analyze each singularity z0 of f I

In the next five problems, analyze each singularity z_0 of f. Is it removable, a pole, or essential? If it is a pole, what is its order? If it is removable, what value should you give the function at z_0 to make it analytic? f(z) = e^z - 1 - z/z^2.

Solution

Given function f(z) has second order singularity at z = 0;

The singularity is a pole and simovable of 2nd order.